What is the difference between area and perimeter?

Perimeter is the distance around the outside (like fencing a farm); area is the space inside (like the land that is farmed).

Why is a cone one-third of a cylinder?

A cone fits exactly three times into a cylinder with the same base and height — you can test it by filling them with sand or water.

Topic guide · JSS 1, JSS 2, JSS 3, SS 1

Mensuration

Area of triangles, trapeziums, parallelograms and circles, and volume of cuboids, cylinders and cones — with π = 22/7 worked examples and practice.

Start the Perimeter of Plane Shapes lesson →

Mensuration explained

Mensuration means measuring: the distance around a shape (perimeter), the space it covers (area) and the space a solid takes up (volume). Area is measured in square units like cm² and volume in cubic units like cm³.

In Nigerian exams, π is usually taken as 227, and many questions use radii like 7 cm or 14 cm so that the answers come out neatly.

Key ideas to remember

Area of a triangle = ½ × base × height; parallelogram = base × perpendicular height.
Area of a trapezium = ½(a + b)h, where a and b are the parallel sides.
Circle: circumference = 2πr, area = πr². Use the radius, not the diameter.
Volume of a cuboid = l × w × h; cylinder = πr²h; cone = ⅓πr²h.

Worked example

Find the circumference of a circle of radius 7 cm. [Take π = 227]

Step 1: Use C = 2πr
C = 2 × 227 × 7 = 44 cm

Final answer: 44 cm

Practice questions

Have a go, then open the answer to check your working. Every answer was checked by the MathPlug maths engine.

Question 1
Find the area of a triangle with base 38 cm and height 6 cm.
- A228 cm²
- B120 cm²
- C44 cm²
- D114 cm²
Show answer and working
1. Step 1: Use ½ × b × h
  ½ × 38 × 6 = 114 cm²
Final answer: 114 cm²
Question 2
Find the volume of a cuboid measuring 8 cm by 4 cm by 9 cm.
- A288 cm³
- B280 cm³
- C32 cm³
- D21 cm³
Show answer and working
1. Step 1: Multiply the three dimensions
  8 × 4 × 9 = 288 cm³
Final answer: 288 cm³
Question 3
Find the area of a circle of diameter 42 cm. [Take π = 227]
- A5,544 cm²
- B132 cm²
- C1,408 cm²
- D1,386 cm²
Show answer and working
1. Step 1: Find the radius
  r = 42 ÷ 2 = 21 cm
2. Step 2: Use A = πr²
  A = 227 × 21 × 21 = 1,386 cm²
Final answer: 1,386 cm²

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Frequently asked questions

What is the difference between area and perimeter?: Perimeter is the distance around the outside (like fencing a farm); area is the space inside (like the land that is farmed).
Why is a cone one-third of a cylinder?: A cone fits exactly three times into a cylinder with the same base and height — you can test it by filling them with sand or water.